Keep in mind that, unlike academia, most of the education sector (primary/secondary) regards "teaching" as a skill that can and should be acquired--usually through some combination of formal education and practical training--before the teacher actually sets foot into the classroom.
So yes a wealthy school might value a PhD (slightly) but they will value an actual track record (and actual teacher certification) more. Do you think parents are going to pay top dollar for "unqualified" teachers? And why should they hire you when they can hire (say) someone from the local school system who's done well?
Anyway, if you want to be a high school teacher, you'll have to start with certification like everyone else, and work your way up (also like everyone else). And sorry to say your PhD could be a liability if it makes the school question whether you really want to be there.